Passengers using elevators can generally give calls to elevators either in an elevator car and/or in an elevator lobby. Elevator lobbies are typically provided with up/down pushbuttons, by means of which a passenger can order an elevator to the call floor and simultaneously indicate his/her travel direction. After the elevator has arrived at the call-giving floor, the passenger moves into the elevator car and indicates his/her destination floor with the pushbuttons of the car panel in the elevator car. To a constantly increasing extent so-called destination call systems are used in high-rise buildings, in which systems a passenger indicates his/her destination floor already before going into the elevator car. For giving destination calls a passenger uses a destination call-giving apparatus. A destination call-giving apparatus is generally provided with a so-called decimal numeric keypad and with a display. If a passenger is going e.g. to floor 24, he/she keys into the decimal numeric keypad first the number 2 and then the number 4. The destination call apparatus sends the data about the call-giving floor and about the aforementioned floor 24 to the control system of the elevator system. After it has received a destination call, the control system of the elevator system allocates the optimal elevator for the use of the passenger and communicates to the user the elevator allocated to him/her. For example, the control system can send information identifying the allocated elevator to a call-giving apparatus, on which appears e.g. the text “Elevator B”. A problem has been that it has been difficult for a user to locate the elevator allocated to him/her. For example, in a large or busy elevator lobby it is not always easy for a user to quickly see and identify an elevator allocated to him/her. It is uncomfortable for a user if he/she must search for his/her elevator. This can also result in unnecessary extra traffic in the elevator lobby. The aforementioned types of problems have occurred more particularly when the call-giving apparatus is a portable call-giving apparatus, e.g. a mobile phone. Since the system does not know the location of the user, it has not been possible to indicate to him/her simply where the elevator allocated to him/her is located.